Prediction of the Natural Gas Compressibility Factor by using MLP and RBF Artificial Neural Networks

Neven Kanchev; Nikolay Stoyanov; Georgi Milushev

doi:10.2478/msr-2025-0001

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Prediction of the Natural Gas Compressibility Factor by using MLP and RBF Artificial Neural Networks

Measurement Science Review

Volume 25 (2025): Issue 1 (February 2025)

By: Neven Kanchev, Nikolay Stoyanov and Georgi Milushev

Open Access

|Feb 2025

Figures & Tables

Effect of the number of hidden neurons of the MLP-ANN for the LM algorithm.

Effect of the number of hidden neurons of the MLP-ANN for the SCGD algorithm.

Table 1.

Comparative analysis of LM and SCGD algorithms.

Algorithm	R²	MSNE	RMSE	MAE
LM	0.99032	0.0581	0.1206	0.087
SCGD	0.94229	0.0953	0.1543	0.1144

Table 2.

Tested combination of activation functions of MLP-ANN.

Activation function hidden layer	Activation function output layer	R²	MSNE	RMSE	MAE
tansig	tansig	0.99032	0.0581	0.1206	0.087
tansig	purelin	0.99219	0.3866	0.3109	0.2363
logsig	tansig	0.94438	0.1034	0.1607	0.1072
logsig	purelin	0.98062	0.6353	0.3985	0.3117
purelin	tansig	0.82875	0.1136	0.1685	0.1184
logsig	logsig	0.83831	0.2505	0.2502	0.1884
tansig	logsig	0.85305	0.2536	0.2518	0.195
purelin	logsig	0.68672	0.2955	0.2718	0.2067

Scatter plot of predicted values versus observed values for MLP-ANN.

Plot of predicted values versus observed values for MLP-ANN.

Scatter plot of predicted values versus observed values for RBF-ANN.

Plot of predicted values versus observed values for RBF-ANN.

Table 3.

Influence of hidden neurons of RBF-ANN.

Spread value	Neurons	MSE	MSNE	RMSE	MAE
0.1	140	0.99899	0.00073	0.0135	0.0075
0.3	140	0.99742	0.0019	0.0215	0.0108
0.5	140	0.99477	0.0038	0.0306	0.014
0.1	130	0.9973	0.0019	0.022	0.0141
0.3	130	0.99257	0.0053	0.0365	0.0181
0.5	130	0.99272	0.0052	0.0361	0.0177
0.1	120	0.9936	0.0046	0.0339	0.02
0.3	120	0.98875	0.0081	0.0449	0.0268
0.5	120	0.98833	0.0084	0.0457	0.0266

Table 4.

Comparison between MLP and RBF models.

Type ANN	R²	MSNE	RMSE	MAE
MLP-ANN	0.99032	0.0581	0.1206	0.087
RBF-ANN	0.99899	0.000729	0.0135	0.0075

Comparison of relative errors of the MLP-ANN and the RBF-ANN model.

References

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Articles in this issue

DOI: https://doi.org/10.2478/msr-2025-0001 | Journal eISSN: 1335-8871

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Language: English

Page range: 1 - 9

Submitted on: Jul 18, 2024

Accepted on: Jan 8, 2025

Published on: Feb 24, 2025

Published by: Slovak Academy of Sciences, Institute of Measurement Science

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

natural gas,

compressibility factor,

artificial neural network,

multi-layer perceptron,

radial basis functions

Related subjects:

Engineering,

Electrical engineering,

Control engineering, metrology and testing

© 2025 Neven Kanchev, Nikolay Stoyanov, Georgi Milushev, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 25 (2025): Issue 1 (February 2025)

Prediction of the Natural Gas Compressibility Factor by using MLP and RBF Artificial Neural Networks

Figures & Tables

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Table 1.

Table 2.

Fig. 6.

Fig. 7.

Fig. 8.

Fig. 9.

Table 3.

Table 4.

Fig. 10.

Paradigm

My account